Capillary compression induced outstanding n-type thermoelectric power factor in CNT films towards intelligent temperature controller

One-dimensional carbon nanotubes are promising candidates for thermoelectrics because of their excellent electrical and mechanical properties. However, the large n-type power factor remains elusive in macroscopic carbon nanotubes films. Herein, we report an outstanding n-type power factor of 6.75 mW m−1 K−2 for macroscopic carbon nanotubes films with high electrical and thermal conductivity. A high-power density curl-able thermoelectric generator is fabricated with the obtained carbon nanotubes films, which exhibits a high normalized power output density of 2.75 W m−1 at a temperature difference of 85 K. The value is higher than that of previously reported flexible all-inorganic thermoelectric generators (<0.3 W m−1). An intelligent temperature controller with automated temperature-controlling ability is fabricated by assembling these thermoelectric generators, which demonstrates the potential application of the carbon nanotubes films in automated thermal management of electronic devices where requires a large thermoelectric power factor and a large thermal conductivity simultaneously.


Calculation of the weighted mobility
The weighted mobility ( ) was estimated from the electrical conductivity and thermopower, which reflects the carrier mobility weighted by the density of states as follows： Where  ,  , h, e, σ , and S are the electron mass, Boltzmann constant, Planck constant, electronic charge, electrical conductivity, and Seebeck coefficient, respectively.The weighted mobility gives nearly the same information about charge carrier mobility as the Hall mobility and thus it has been widely used to investigate charge carrier transport mechanisms in previous literatures. 1,2,3,4 FiS1.The TEM images of CNT.
High-resolution transmission electron microscopy (TEM) images showed that the majority of the CNTs were multi-walled carbon nanotubes (MWCNTs).
Similar results have been reported in previous works that MWCNTs were obtained when the same method was used in the synthesis process. 5As it is known that the band gap is inversely proportional to the diameter of CNTs, MWCNTs typically exhibit metal-like electrical properties. 6,7 ,11,12,13 This is also consistent with the results of the Raman spectra shown in Figure S2 that IG/ID of CNT-e is slightly lower than that of CNT-o.  The electric conductivity of the film was measured by commercial equipment (NETZSCH, SBA-458, Germany) with a four-probe method.All measurements were carried out at room temperature under argon protection and the CNT film samples were cut into strips 20 mm long and 4 mm wide.The electrical conductivity (σ) of the samples was calculated by the equation:  1  ⁄   ⁄ , where ρ was the resistivity, L was the length of the sample between the electrodes, R was the resistance and A was the cross-sectional area of the sample.This method has been widely used for the electrical conductivity measurement of films.5,7,9,10,14,15,16,17  To understand the change of the electrical conductivity and the Seebeck coefficient of the CNT films during compressing, it would be better to focus on the "effective" conducting components which are CNT in the films.It is believed that the change in carrier mobility is responsible for the high power factor rather than the density of states.
The increase of the electrical conductivity of CNT films was due to the decrease of the porosity.SEM images in Figure S5 indicated that the CNT films became dense after being compressed.The packing density of CNTs in the films before compressing was lower than that of the CNTs in the films after compressing (Figure 1a, 1b and Figure S5), which subsequently resulted in lower electrical conductivity of the CNT films before compressing than that of the CNT films after compressing (Figure 1c).The electrical conductivity changes of the CNT films before and after compressing could be well understood with Maxwell-Eucken's equation as shown below: where P is the porosity,  is the total electrical conductivity of a porous material,  is the intrinsic electrical conductivity of the materials, and β is the constant number determined by the conditions of the pores.20 When the CNT films were compressed, the porosity decreased (the packing density increased).The well alignment and dense packing of CNT resulted in the improvement of the carrier mobility in the films.Therefore, the electrical conductivity of the compressed CNT films was higher than that of the CNT films before compressing.Similar results have also been reported in previous works that the electrical conductivity is inversely proportional to the thickness (proportional to the density) of CNT films or their composite films after compressing.21,22,23,24,25,26 In the meanwhile, the compressing process was a physical process, which would not change the chemical environment of a single CNT.Ultraviolet Photoelectron Spectroscopy (UPS) was performed with gold as a reference to identify the work function change of CNT-e and CNT-e/c films (Figure S9).The obtained work function of CNT-e film and CNT-e/c film exhibited similar values, indicating that the chemical environment of the CNT remained constant (the Fermi energy level is unchanged) before and after compressing.In addition, the pressure used in this work was only ~100 MPa which was far behind the pressure required to change the cylinder structure of a single CNT (serval GPa).27,28,29 Therefore, the Seebeck coefficient of the CNT films changed little after compressing.9,10,16,17 The increased electrical conductivity and maintained Seebeck coefficient resulted in the increase of thermoelectric power factor of CNT films after compressing in Figure 2d in the original manuscript.
The energy-filtering effect usually emerges from the barrier blockage of low-energy carriers by the potential barrier, resulting in a significant increase in the Seebeck coefficient, while the electrical conductivity remains constant. 30,31  energy filtering effect was usually observed in carbon nanotubeorganic/inorganic composites, as reported in previous literature. 32,33 owever, this effect may not fulfill the scenario of CNT only films in this work since the Seebeck coefficient of the CNT films maintained nearly constant before and after compressing (Figure 2c).It is challenging to get the accurate value of carrier mobility for CNT films due to the quantum confinement effect as reported by Tanabe et al. in literature. 34,35 n addition, the contained Fe nanoparticles made the Hall measurement data of the CNT films worse.Therefore, we used weighted mobility reported by Snyder's group to evaluate the variation of carrier mobility in CNT films, since the weighted mobility had a similar trend with the Hall mobility, as reported in the previous literature. 1,3,4,36 Th weighted mobility of the obtained matched well with the previously reported literature for CNT. 37e weighted mobility of CNT films after PEI treatment exhibited a slight decrease, as shown in Figure S13.The slightly reduced weighted mobility can be attributed to the introducing of non-conducting PEI molecules, as suggested in the previous literature. 10,38 e S14.The thermoelectric performance between the front and back surfaces of CNTe/c-PEI films.The theoretical output power ( ) was calculated from the equation of

𝑃
, where  was the resistance of TEG.When  was 56 Ω and the temperature difference was 85 K, the  was 47.4 μW, which was larger than the experimental output power (29.7 μW) of SP-TEG/par.The output power of SP-TEG/par measured experimentally was only 60.1 % of the theoretical output power.The reason for experimental output power being lower than the theoretical values can be attributed to the fact that the poor heat dissipation at the cold side results in the higher temperature of the cold side compared to the ambient temperature, thus leading to a lower temperature difference between the hot side and the cold side of the TEG.The same issue has also been reported in the previous literature with low experiment to theory values. 39,40,41

Materials PF
Ref .

Figure S2 .
Figure S2.The Raman spectra of CNT-o films and CNT-e films.

Figure S3 .
Figure S3.The TGA curve of CNT-o films and CNT-e films.

Figure S4 .
Figure S4.The Raman spectra of CNT-o films, CNT-e films, CNT-o/c films and CNT-e/c films.

Figure S6 .
Figure S6.The schematic of the anisotropic electrical conductivity measurements for CNT films.

Figure S7 .
Figure S7.The TE properties in the parallel direction of CNT-o films (a) and CNT-e (b) films as a function of compressing time.

Figure S8 .
Figure S8.The density of the CNT-e films before and after compressing.

Figure S9 .
Figure S9.UPS results of CNT-a and CNT-e/c films.The work function was obtained by the equation:  ℎ | |  , where  was the work function, ℎ was the incoming photon energy from the He I source of 21.2 eV, and | |  was the difference in energy between the onset of the secondary electrons and the Fermi edge. 6, 7The obtained work function of CNT-e film and CNT-e/c film exhibited similar values, indicating that the chemical environment of the CNT remained constant (the Fermi energy level is unchanged) before and after compressing, which resulted in the maintenance of the Seebeck coefficient.

Figure S11 .
Figure S11.The TE properties in the perpendicular direction of CNT-e film as a function of compressing time.

Figure S13 .
Figure S13.The weight mobility in the parallel direction (µ∥) of CNT-o/c films, CNT-e/c films, CNT-o/c-PEI films and CNT-e/c-PEI films.

Figure S15 .
Figure S15.The TGA curve of CNT-e/c films and CNT-e/c-PEI films.

Figure S16 .
Figure S16.The TE properties in the perpendicular direction of CNT-o/c-PEI films (a) and CNT-e/c-PEI films (b) as a function of vapor treatment time.

Figure S17 .
Figure S17.The thermal conductivity of CNT films.

Figure S18 .
Figure S18.Schematic of thermal conductivity in different directions of carbon nanotube films.

Figure S19 .
Figure S19.The ZT value of CNT films.

Figure S20 .
Figure S20.The TE properties in parallel direction of CNT-e film as a function of vapor treatment time for Me-TBD (a), TBD (b) and TMG (c).

Figure S21 .
Figure S21.Comparison of comprehensive performance of CNT-e/c films including σ ∥ , PF ∥ flexibility, mechanical strength and temperature stability.

Figure S22 .
Figure S22.The strain-stress of CNT films in parallel (a) and perpendicular (b) direction.

Figure S23 .
Figure S23.The resistance varied as a function of bending cycles of a strip of CNT-e/c and CNT-e/c-PEI films.

Figure S24 .
Figure S24.COMSOL simulation results for output power of perpendicular (a), annular (b) and parallel TEG (c) as a function of structural variations with FF=0.5.

Figure S25 .
Figure S25.COMSOL simulation results for output power of parallel, perpendicular and annular TEG as a function of FF.

Figure S26 .
Figure S26.The open-circuit voltage in different temperature differences of SP-TEG/par.The theoretical open-circuit voltage ( ) was calculated from the equation of    | | ∆, where N was the number of p−n modules and  and  were the Seebeck coefficients of p-type and n-type TE materials, respectively.When the temperature difference was 85 K, the maximum experimental open-circuit voltage ( ) was 81.5 mV, which was lower than VTH (103 mV, Figure S26).

Figure S27 .
Figure S27.The voltage-current curves of per-TEG (a) and ann-TEG (c) at different temperature differences.The output power of per-TEG (b) and ann-TEG (d) as a function of load resistance.

Figure S28 .
Figure S28.The output power stability of par-TEG (in air, in water and in water after encapsulation).

Figure S29 .
Figure S29.Schematic of the vapor doping process.

Table S1 .
The sheet resistance of CNT-e/c films.

Table S2 .
The maximum weighted mobility of CNT-o/c-PEI films and CNT-e/c-PEI films.

Table S3 .
The thermal conductivity of CNT-o films, CNT-e films, CNT-o/c films CNT-e/c films, CNT-o/c-PEI films and CNT-e/c-PEI films.

Table S4 .
Comparison of calculated effective thermal conductivity eff for representative materials with a Δ of 1 K at 300 K.

Table S5 .
Comparison of in-plane ZT values of CNT films at room temperature.

Table S6 .
Physical properties of the materials used in finite-element analyses.